1. Field
The invention relates to a method for determining the dependence of a first measuring quantity on a second measuring quantity wherein
(a) the second measuring quantity is periodically modified with a frequency and
(b) the first measuring quantity changing accordingly is measured.
2. State of the Art
One example for the use of the invention is measuring the surface photo voltage of a material as first measuring quantity in dependence on the wavelength of the excitation light as second measuring quantity. When the surface of a semiconductor is exposed to light, a surface photo voltage is generated at the surface of the material, this surface photo voltage being a function of, inter alia, the diffusion length of the charge carriers in the material and being indicative thereof. The surface photo voltage is also a function of the wavelength of the excitation light. The longer the wavelength of the light, the higher is the transmission ability of the material for the light and the deeper penetrates the light into the material. The relationship between diffusion length and surface photo voltage is complicated. However, the relationship can be approximately linearized when operating either with constant intensity of the light or with constant output signal, that means when the measurement is operated at defined operating points. The measurement of the surface photo voltage can be used for detecting irregularities of the material, for example of a semiconductor wafer. For this purpose the surface photo voltage of the material is investigated point by point throughout the surface of the material.
Through EP-A-0 077 021 an apparatus is known for nondestructively measuring characteristics of a semiconductor wafer by means of a SPV-method. The wafer is irradiated by a pulsated light beam from a light source. The pulse frequency of the light beam is changeable by means of an oscillator. The light beam generates a photo voltage at the surface of the wafer. This photo voltage is picked up by capacitance coupling by an electrode. For noise suppression the photo voltage picked up by capacitance coupling is amplified by an lock-in amplifier. Through a signal processing unit the frequency of the oscillator (and thus the pulse frequency of the light beam) is determined and monitored. Furthermore, the signal processing unit determines the measured photo voltage in dependence on the pulse frequency. The pulse frequency is continuously increased and the photo voltage is measured. log Vph is shown as a function of log f at a display. At a critical frequency the dependence of the photo voltage on the pulse frequency changes in a characteristic manner. This critical frequency is indicative of the carrier lifetime to be measured, the carrier being generated by the light beam.
U.S. Pat. No. 5,663,657 also discloses a SPV-method for investigating a semiconductor wafer, in which the diffusion length of minority carrier is determined. A region of the wafer is exposed to light of different wavelength in several steps and the resulting photo voltage is measured. The photo voltage is determined as a function of the penetration depth of the excitation light, the penetration depth being a function of the wavelength of the light.
The surface photo voltages are very small and subject to strong noise. Therefore, the measuring is effected by means of a xe2x80x9clock-inxe2x80x9d technique. The intensity of the excitation light is modulated with a modulation frequency and modulation phase. This results in a corresponding modulation of the measuring signal, as far as this results from the excitation by the light. By Fourier transformation of the measuring signal the component of the measuring signal is determined, which component, with regard to the frequency and the phase, corresponds to the modulation frequency and the modulation phase. Thus, the noise is suppressed such that even a very weak signal can be detected. Then the measurement is carried out for each investigated point of the material at various wavelength of the excitation light.
This measuring method takes very long time. When using the lock-in technique, a certain number of periods of the modulation frequency, for example five, is required for each measurement. The modulation frequency is limited by the material: When exposed to light, it takes a certain time before a state of equilibrium is reached in the material and a measurement of the surface photo voltage is useful. When the measurement then has to be carried out for each scanned point of the surface at various wavelengths and many points of the surface are to be scanned, this results in a measuring time which is intolerably long. Thus, in practice, when testing semiconductor wafers by surface photo voltage, only a very restricted number of measuring points are measured at a very restricted number of wavelengths.
It is the object of the invention to reduce the measuring time in these cases and in the case of methods for determining the dependence of a first measuring quantity (Y) on a second measuring quantity (P), which methods have similar problems, noise being suppressed as well.
According to the invention this object is achieved in a method of the above mentioned type in that
(c) from the obtained measuring signal of the first measuring quantity the components of the first measuring quantity are determined with at least a plurality of frequencies and
(d) from the components thus determined the first measuring quantity is reconstructed for at least a plurality of values of the second measuring quantity by signal processing.
Regarding the example of the surface photo voltage, thus, according to the invention, a modulation of the excitation light is not effected at a predetermined wavelength, which leads to a modulation of the surface photo voltage as xe2x80x9cfirst measuring quantityxe2x80x9d. The wavelength of the excitation light is rather varied as xe2x80x9csecond measuring quantityxe2x80x9d periodically throughout a scanning range with a frequency f0. This results in a periodical measuring signal. The component of the frequency f0 and the higher harmonics 2f0, 3f0 . . . up to an upper limit frequency Nf0 are obtained from this measuring signal. This also suppresses noise. Then, by inverse Fourier transformation, the first measuring quantity (for example surface photo voltage), then free from noise, can be reconstructed from the thus determined components in dependence on the second measuring quantity (for example wavelength) for at least a plurality of values of the second measuring quantity.
The photon density of the excitation light as a function of the wavelength can be measured additionally and taken into account in the calculation. This photon density can possibly by measured once and being calibrated. However, a determination of the photon density and of its dependence on the wavelength can be repeated in certain time intervals, not necessarily with the modulation frequency. However, it is not necessary to bring this photon density physically to a constant value at the various measuring points and wavelengths.
A preferred device for carrying out the method is subject matter of claim 9.
Modifications of the invention are subject matter of the sub-claims.